If you say so
The way it's written in the text it could IMHO be either. That Mug of Fiery Fizzybrew Beer I mentioned also teaches a custom move, on the condition that the Mug is held by the Pokémon. That's why I asked.

But when I get hold of a PC/laptop I'll go ahead and treat it as a regular CM. And blame you if it happens to be otherwise haha